### Prove that every tree with two or more vertices is bichromatic?

Prove that the maximum vertex connectivity one can achieve with
a graph G on n.
01.
Define a bipartite graph. Prove that a graph is bipartite if and
only if it contains no
circuit of odd lengths.
Define a cut-vertex. Prove that every connected graph with three
or more vertices
has at least two vertices that are not cut vertices.
Prove that a connected planar graph with n vertices and e edges
has e - n + 2 regions.
02.
03.
04.
Define Euler graph. Prove that a connected graph G is an Euler
graph if and only if
all vertices of G are of even degree.
Prove that every tree with two or more vertices is
2-chromatic.
05.
06.
07.
Draw the two Kuratowski's graphs and state the properties common
to these graphs.
Define a Tree and prove that there is a unique path between
every pair of vertices in a
tree.
If B is a circuit matrix of a connected graph G with e edge arid
n vertices, prove
that rank of B=e-n+1.
08.
09.